Simple metal sorption model for heterogeneous sorbents: Application to humic materials

A semiempirical equilibrium model to simulate proton and metal binding to h eterogeneous sorbents is presented. In the simple metal sorption (SiMS) mod el, proton and metal binding reactions to a heterogeneous surface are conce ptualized as reactions with a single, composite "site," with empirical corr ection factors to the equilibrium constants that are represented as simple power functions of hydrogen ion concentration, metal-to-ligand ratio (Me-T/ L-T), and ionic strength (I). That is, the observed metal-binding equilibri um constant, K-Me,K-app is represented as K-Me,K-app = K-Me{H+}(alpha)(Me-T /L-T)I-beta(phi). The validity of this approach is tested by fitting the mo del to a hypothetical multiligand data set and three data sets from the lit erature involving proton and metal binding to humic materials (two data set s involving Cu2+ and H+ binding, and one data set for binding of Co2+ and H +). Independent data sets involving Cu2+ binding are used for model predict ion. The fitted models are used to contrast the three humic materials in te rms of acid/base characteristics and H+/Me exchange ratios. A theoretical l imitation of the model is that it does not satisfy the Gibbs-Duhem equation for thermodynamic consistency. The major advantages of the SiMS model are simplicity (i.e., few fitting parameters), flexibility in describing proton and metal binding to heterogeneous sorbents, and ease of application (mode l results presented in this paper were done on a standard spreadsheet). The model is presented not as a new development in the conceptual understandin g of metal-humate interactions, but rather a practical engineering tool tha t can easily be incorporated into general fate and transport models.